Q5) (a) Solve by using Laplace transform the partial differential equation 8², =9. y(0,t)= 0, y(2,t) = 0, y(x,0) = 20 sin 2x-10 sin 5mx and " dy(x,0) Ət =0

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y" +…

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Q: Q4) a) Find the tangent plane and normal line of the surface f(x, y, z) = x? + y²e* + z? = 3 at…

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Q: Q.2) The basts of the equatioon y'' + y" = 0,are: b) 1,1.e a) 1,1.e c) 1, x,e²* d) 1,x.e" 0 about

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Q: Solve the simultaneous ODES (a) (b) y"(t) + y'(t)- 2y(t) = sin t., x'(t) + x(t)- 3y(t) = 0 -

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Q: e the differential equatons 2x + X dx I+ x²y2 I+ (xy)2/ ay dy

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Q: Can you solve this? p(t)y'' + q(t)y' + r(t) = g(t) + f(t)

A: This is a general question of second order differential equation. It is a non homogeneous…

Q: Given h(x) = f(x) · g(x) f(x) • j(x) = %3D g(x) - 5, the equation of the tangent line of f is y – 7…

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Q: 1 y" + (у)? %3D уу' у(0) %3D 1, у'(0) -

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Q: b) Determine the characteristic equation for y" + 3y + 2y = 0. c) Find the general solution for y" +…

A: The differential equation is:To Do:Determine the characteristic equation and solution to the given…

Q: Evaluate the following integral -1.6 Ax? + Bx + C + 5 dp- I = sin 2x (i) Trapezoidal Rule (ii)…

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Q: Solve using Laplace Transfrom Method: y'''+3y''+3y'=y       y(0)=7,   y'(0)=-7,    y''(0)=11

A: Given function is, y'''+3y''+3y'=y    y(0)=7,   y'(0)=-7,    y''(0)=11 Now, using the…

Q: (c) Given T" = 6x²y³ – cosx + 5y² – siny + 10x² – e-3x," determine (1) T' = S(T")ax T' = S(T")ay…

A: GivenT"=6x2y2-cos x+5y2-sin y+10x2-e-3xwe know…

Q: y" (t) + 2y' + y(t) = 8t²e-t.

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Q: Find y as a function of a if y(0) = 1, y'(0) = 9, y" (0) = -191. y(r) = j y"-7y" -y + 7y=0,

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Q: Determine the value of k, so that (1 + ekx²)y = 1, be an implicit solution of the nonlinear ODE y' =…

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Q: Classify each of the equations above as autonomous, separable, linear, homogeneous, Bernoulli, or…

A: "Since you have posted a question with multisubparts, we will solve first three parts for you. To…

Q: (1+x2) y + 8xy' +6y=0

A: We have, This differential equation doesn't have a constant coefficient for the second derivative is…

Q: Suppose A is changed to A' .How large a relative change can this change produce in the solution to…

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Q: solve the non-homogenous equation y” – 2y’ = t + e^t

A: The given equation is a non-homogeneous second order differential equation. The general solution of…

Q: Q.4) The Wronskian W(e~2", e",e²), is: a) 12e b) –12e c) 6e² d) -6e"

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Q: tY"(t) + (1 – 2t)Y'(t) – 2 Y(t) = 0, Y(0) = 1, Y'(0) = 2 %3D

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Q: . Can the equation x + y + z = sin(ryz) be solved uniquely in form = f(x, y) in a neighborhood of…

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Q: y" - 2y' + y = 4e-t + 2et, where y(0) = -1, y'(0) = 2

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Q: Solve for the higher order DE number 2

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Q: 8. (y – In æ) dæ + (x +1) dy = 0, y(1) = 10 Ghenoral Form : y' + Pixly= Q(x) I (x): PLk) du : Final…

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Q: (x, y) = x + y' + kxy.

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Q: Consider the Riccatti equation  v'= v^2-7v/x +8/x^2 a) Use the substitution  v= y'/y  obtain the…

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Q: Can you explain how all A B C D terms are calculated

A: Solution of the given question is like as

Q: Consider the Riccatti equation v'=v2-(7/x)v+8/x2 a) use the substitution v=-y'/y

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Let F(x) = X S 12 Enter the exact answers. (a) F(12) = i (b) F' (12) = 2 √² + 25 dt. Find the…

A: Let . To find the following.

Q: 7) Determine an eq ,in (x) and (y) , and then find a) y sec 1t , x csc-1t b) y = (sin 0)* ,x = (cos…

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